I play video games to lose myself in a cool story that I control to an extent. I like games that have stories, where stuff happens and you're actually drawn in.
Reading provides the real deep fantasy experience, but what video games lack in depth of story, they make up for in control factor. It's so fun and awesome to be something else for a while.
Also, I always expand the stories as I go along. Games like Doom and Quake, when I was younger, had no real story, but I was coming up with cool stuff left and right to explain what was going on.
Even games like GTA, which are very well written for video games, I expand on in my head. What might appear as mayhem and car crashes to some, are quite more in my head.
Another aspect of video games, that is not story based, is they are something to overcome and succeed in, but are also simple and fun to look at. Older games like Donkey Kong Country or any side scrolling Mario title, aren't so much about story, but are just about cool stuff to do and see.
Video games, in moderation, are good for kids as well. When you play games, totally different brain processes are going on than when you just stare at the TV like a lump.
Finally, good video games provide stimulation to people who are not good at sports, or don't care to play them. And for the casual gamer that is also a sports fan and has a social life, they are really fun to just sit back and play while high or drunk during a quiet evening. Or sober.